We propose a Markovian quantum model for the time dependence of the pressure-induced decoherence of rotational wave packets of gas-phase molecules beyond the secular approximation. It is based on a collisional relaxation matrix constructed using the energy-corrected sudden approximation, which improves the previously proposed infinite order sudden one by taking the molecule rotation during collisions into account. The model is tested by comparisons with time-domain measurements of the pressure-induced decays of molecular-axis alignment features (revivals and echoes) for HCl and CO₂ gases, pure and diluted in He. For the Markovian systems HCl-He and CO₂-He, the comparisons between computed and measured data demonstrate the robustness of our approach, even when the secular approximation largely breaks down. In contrast, significant differences are obtained in the cases of pure HCl and CO₂, for which the model underestimates the decay rate of the alignment at short times. This result is attributed to the non-Markovianity of HCl-HCl and CO₂-CO₂ interactions and the important contribution of those collisions that are ongoing at the time when the system is excited by the aligning laser pulse.